University of Tehran
Electrical Machines II
Homework#7&8 (Induction Machines)
1- How the induction machines can work as an autotransformer? What are the benefits
and deficiencies of this autotransformer in comparison with the common
autotransformers?
2- How the induction machines can be used as the frequency changer? What are the
application problems of this device?
3- Explain the methods for driving (Starting and controlling of the speed) the wound –
rotor induction motors.
4- -A 3-phase induction motor works at the nominal conditions. Suddenly, one of the
phases is disconnected. Discuss the events occurs to the machine. Also, explain the
performance of the single-phase motors (How the circular field is appeared).
5- Why the inductances are neglected when we are going to calculate the efficiency of
the motors, while they have their impedance and influence the current drawn from the
network?
6- A 3-phase, 200-hp, 3300-V, star-connected induction motor has the following
equivalent circuit parameters per phase:
R1 = R2’= 0.8Ω, X1 = X2’ =3.5Ω
a) Calculate the slip at full load if the friction and windage loss is 3kW.
b) How much extra rotor resistance would be necessary to increase the slip to three times
this value with the full-load torque maintained?
c) How much extra stator resistance would be necessary to achieve the same object and
what loss of peak torque would result?
7- A 3-phase, 6-pole, 50-Hz induction motor has a peak torque of 6Mm and a starting
torque of 3Nm when operating at full voltage. Maximum torque occurs at a slip of
25%. When started at 1/3 of normal voltage, the current is 2A.
(a)What is the mechanical power, at peak torque when operating at normal voltage?
(b) What maximum torque would the machine produce at 1/3 of normal voltage?
(c) What starting current would the machine take when supplied with normal voltage?
(d) What extra rotor-circuit resistance, as a percentage, would be required to give
maximum torque at starting and what would then be the current, in terms of that at peak
torque without external resistance?
8- A 140-V, 3-phase, 6-pole, 50-Hz, delta-connected induction motor has the following
equivalent-circuit parameters at normal frequency:
R1 = 0.2 Ω, R2’= 0.18 Ω, x1 = x2’ = 0.58 Ω, all per phase
(a) The machine is subjected in service to an occasional fall of 40% in both voltage and
frequency. What total mechanical load torque is it safe to drive so that the machine just
does not stall under these conditions?
(b) When operating at normal voltage and frequency, calculate the speed when delivering
this torque and the power developed. Calculate also the speed at which maximum torque
occurs.
(c) If V and f were both halved, what would be the increase in starting torque from the
normal direct-on-line start at rated voltage and frequency?
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University of Tehran
Electrical Machines II
Homework#7&8 (Induction Machines)
(d) If now the machine is run up to speed from a variable-voltage, variable-frequency
supply, calculate the required terminal voltage and frequency to give the 'safe' torque
calculated above: (I) at starting and (II) at 500 rev/min.
(e) Repeat (d) for the machine to develop a torque equal to the maximum value occurring
at rated voltage and frequency. In both (d) and (e), the criteria are that the air-gap flux per
pole is maintained constant for any particular torque.
9- The values of E1, XM and x'2 for a particular induction motor are known at a frequency fbase.
(a) Develop the expressions which show that the rotor current and torque are independent
of the supply frequency but depend on the slip frequency, f2; providing that the flux per
pole (E1/f) is constant.
(b) Show also, independently of the above, that for any given primary current I1, the rotor
current I'2 is governed by f2 and explain how this is related to the constant-flux condition.
(c) Finally, derive the expression for the slip s = f2/f at which maximum torque occurs for
a constant-current drive and hence show that the maximum torque capability is
independent of both supply and slip frequencies.
10- A 3-phase, double-cage-rotor, 6-pole, 50-Hz, star-connected induction motor has the
following equivalent-circuit parameters per phase:
Z1 = 0.1+j0.4 Ω, Z’2 = 0.3+j0.4 Ω, Z’3 = 0.1+j1.2 Ω, all at standstill
Find, in terms of the line voltage V1, the torque at 980rev/min:
(a) Including the outer-cage impedance;
(b) Neglecting the outer-cage impedance.
(c) What is the starting torque?
11- A 208-V, 60 Hz, six-pole Y-connected 25-hp design class B induction motor is tested
in the laboratory, with the following results:
No load: 208 V, 22.0 A, 1200 W, 60 Hz
Blocked rotor: 24.6 V, 64.5 A, 2200 W, 15 Hz
DC test: 13.5 V, 64 A
Find the equivalent circuit of this motor, and plot its torque-speed characteristic curve (Show
the important points in the plot with detail). Hint that in the Class B motors, X1 = 0.4Xbrt.
12- A 460-V, four-pole, 50-hp, 60-Hz, Y-connected three-phase induction motor develops
its full-load induced torque at 3.8 percent slip when operating at 60 Hz and 460 V.
The per-phase circuit model impedances of the motor are:
R1 = 0.33 Ω , XM = 30 Ω , X1 = 0.42 Ω , X2 = 0.42 Ω
Mechanical, core, and stray losses may be neglected in this problem.
(a) Find the value of the rotor resistance R2.
(b) Find Tmax, Smax, and the rotor speed at maximum torque for this motor.
(c) Find the starting torque of this motor.
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University of Tehran
Electrical Machines II
Homework#7&8 (Induction Machines)
Project 7 and 8 (Bonus)
Do research about one of the following topics:
1- Find the methods for driving the squirrel-cage induction motors for the industrial
purposes.
2- Explain the brake-mode of operation for induction motors. What happens to the motor
when operate at this mode? What are the possible solutions for these problems?
3- What are the Linear Induction Motors (LIM) and their application?
4- Every new issue about the induction machines!
Happy Christmas!
Good Luck.
H.Ahmadi (h.ahmmadi@ece.ut.ac.ir)
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